Even those with insurance visited the doctor less often over the study’s 10-year period. The report shows that Maine’s uninsured are going without care despite free care offered at Maine hospitals, said Mitchell Stein, policy director for the progressive advocacy group Consumers for Affordable Health Care.

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Meanwhile, residents with health insurance coverage are increasingly burdened with a higher share of health care costs, such as under high-deductible plans, he said.

Edmund Haislmaier, a senior research fellow in health policy at the Heritage Foundation, a conservative policy group in Washington, D.C, took issue with the researchers’ assumptions.

“This is significant only if you share the author’s premise, which is that everyone should have everything they need in health care totally free at the point they receive care, and that anything less than that is inadequate,” he said. “If you start from that premise, which most people don’t, then well it’s a terrible thing that some people don’t have everything handed to them free.”

Compared with other states, Maine performed fairly well on the number of adults reporting cost as a barrier to health care. The share of those ages 19 to 64 with unmet medical needs because of cost was 13.5 percent in Maine in 2010. The national average was nearly 19 percent.

That rate held steady in Maine over the previous decade, while it rose nationally by 6 percent to about one in five adults, the study found.

Stein theorized that an expansion of health coverage under the previous administration, including in Medicaid and the Dirigo Health program, as well as consumer protections related to private insurance, may have buoyed Maine’s performance in the study.

Haislmaier said the report fails to consider factors beyond insurance coverage that affect access to health care, such as geography and low reimbursement rates that discourage primary care doctors from taking Medicaid patients.

“This insurance-equals-access [argument], which I know is a big mantra on the left, it just doesn’t hold up,” he said.

The study was conducted by researchers at the Washington, D.C.-based Urban Institute and funded by the Robert Wood Johnson Foundation. It was based on federal government data compiled from state health department surveys.

On two other indicators of health care access, Maine followed worsening national trends. The study also looked at routine checkups and dental visits.

Nationwide, the number of adults who got a regular medical checkup dropped by 5.1 percent from 2000 to 2010. In Maine, the number dropped by more than 7 percent.

The share of adults who had an annual dental visit fell nearly 4 percent nationally between 2002 and 2010. The drop in Maine was almost 6 percent.

In all, 49 states showed a significant deterioration in at least one of the study’s three measures. West Virginia and the District of Columbia were the exceptions.

Over the past decade, rates of unmet medical needs climbed in 42 states, the share of adults getting routine checkups fell in 37 states, and the number of adults with dental visits dropped in 29 states.

“Our study shows that access to care deteriorated for adults in virtually every state in the country, and that the uninsured experience substantially worse access to care relative to the insured in all states,” Genevieve M. Kenney, the study’s lead author, said in a press release. “This indicates that the health care safety net is not acting as an effective substitute for health insurance coverage when it comes to providing basic health care to the uninsured.”

In Maine, census data show that about 14 percent of adults ages 19 to 64 lack health insurance. Data collected by the Centers for Disease Control and Prevention peg the figure closer to 16 percent. The national average is roughly 21 percent.

The Robert Wood Johnson Foundation used the report to advocate for the landmark federal health reform law passed in 2010. Researchers predicted that if provisions of the Patient Protection and Affordable Care Act are ruled unconstitutional this summer, the downward trends in access will continue.

The law would expand Medicaid coverage and provide subsidies to consumers to offset private insurance premiums and out-of-pocket costs.

Stein agreed that the findings highlighted the need for the Affordable Care Act, which he said would cover the uninsured and make private insurance more affordable.

Haislmaier countered that the reform law will do nothing to put a dent in the rising costs of health care and using new money to pay for subsidies only exacerbates the problem.

“If you already have the most expensive system in the world and you still have problems, why do you need more money to fix the problems? Why can’t you just reprogram the money you’ve got and spend it smarter?” he said.